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easy fractions question

I know I shouldn't have to ask this but its really confusing me.
Why can (e^-x)/(1-e^-x) be written as 1/((e^-x)-1)
can x/1-x always be written as 1/x-1 ? if so can someone provide a simple proof/explanation. cheers.
Original post by Gibus_pyro
I know I shouldn't have to ask this but its really confusing me.
Why can (e^-x)/(1-e^-x) be written as 1/((e^-x)-1)
can x/1-x always be written as 1/x-1 ? if so can someone provide a simple proof/explanation. cheers.

It can't. Evaluate both sides at x=log⁡(2)x = \log(2) to get LHS 1/21−1/2=1\frac{1/2}{1-1/2} = 1, RHS 1−1/2=−2\frac{1}{-1/2} = -2.
Original post by Gibus_pyro
I know I shouldn't have to ask this but its really confusing me.
Why can (e^-x)/(1-e^-x) be written as 1/((e^-x)-1)
can x/1-x always be written as 1/x-1 ? if so can someone provide a simple proof/explanation. cheers.


e−x1−e−x=1ex−1\frac{e^{-x}}{1-e^{-x}}=\frac{1}{e^x-1} by multiplying top and bottom by exe^x
Original post by Gibus_pyro

can x/1-x always be written as 1/x-1 ? if so can someone provide a simple proof/explanation. cheers.


Are you suggesting that x1−x=1x−1\dfrac{x}{1-x} = \dfrac{1}{x-1} If so, no
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Original post by brianeverit
e−x1−e−x=1ex−1\frac{e^{-x}}{1-e^{-x}}=\frac{1}{e^x-1} by multiplying top and bottom by exe^x

thanks , that makes sense

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